The Leray-Schauder index and the fixed point theory for arbitrary ANRs
Andrzej Granas (1972)
Bulletin de la Société Mathématique de France
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Andrzej Granas (1972)
Bulletin de la Société Mathématique de France
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Gottlieb, Daniel H., Samaranayake, Geetha (1995)
The New York Journal of Mathematics [electronic only]
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Obukhovskii, Valeri, Zecca, Pietro, Zvyagin, Victor (2002)
Abstract and Applied Analysis
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R. Dobreńko, Z. Kucharski (1990)
Fundamenta Mathematicae
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Marian Mrozek, James Reineck, Roman Srzednicki (1999)
Banach Center Publications
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In this note we present the main ideas of the theory of the Conley index over a base space introduced in the papers [7, 8]. The theory arised as an attempt to solve two questions concerning the classical Conley index. In the definition of the index, the exit set of an isolating neighborhood is collapsed to a point. Some information is lost on this collapse. In particular, topological information about how a set sits in the phase space is lost. The first question addressed is how to retain...
Dorota Gabor (2000)
Annales Polonici Mathematici
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We study a coincidence problem of the form A(x) ∈ ϕ (x), where A is a linear Fredholm operator with nonnegative index between Banach spaces and ϕ is a multivalued A-fundamentally contractible map (in particular, it is not necessarily compact). The main tool is a coincidence index, which becomes the well known Leray-Schauder fixed point index when A=id and ϕ is a compact singlevalued map. An application to boundary value problems for differential equations in Banach spaces is given. ...
Helga Schirmer (1990)
Fundamenta Mathematicae
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Helga Schirmer (1984)
Fundamenta Mathematicae
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Saveliev, Peter (2005)
Fixed Point Theory and Applications [electronic only]
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Karol Pąk (2009)
Formalized Mathematics
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We present the concept and basic properties of the Menger-Urysohn small inductive dimension of topological spaces according to the books [7]. Namely, the paper includes the formalization of main theorems from Sections 1.1 and 1.2.